Device and method for measuring phase retardation distribution and fast axis azimuth angle distribution in real time

ABSTRACT

Device and method for measuring phase retardation distribution and fast axis azimuth angle distribution of birefringence sample in real time. The device consists of a collimating light source, a circular polarizer, a diffractive beam-splitting component, a quarter-wave plate, an analyzer array, a charge coupled device (CCD) image sensor and a computer with an image acquisition card. The method can measure the phase retardation distribution and the fast axis azimuth angle distribution of the birefringence sample in real time and has large measurement range. The measurement result is immune to the light-intensity fluctuation of the light source.

CROSS-REFERENCE AND RELATED APPLICATIONS

The subject application is a continuation-in-part of PCT internationalapplication PCT/CN2012/000990 filed on Jul. 23, 2012, which in turnclaims priority on Chinese patent application No. CN 201210199435.4filed on Jun. 15, 2012. The contents and subject matter of the PCT andChinese priority applications are incorporated herein by reference.

TECHNICAL FIELD OF THE INVENTION

The subject application relates to polarization measurement, especiallyone device and method for measuring phase retardation distribution andfast axis azimuth angle distribution of the birefringent component inreal time.

BACKGROUND OF THE INVENTION

Birefringent component is widely used in many domains, such as polarizedillumination system of immersion lithography, phase shiftinginterferometry and biological optics. The phase retardation and fastaxis azimuth angle are two important parameters of birefringentcomponent. The phase retardation distribution and fast axis azimuthangle distribution of the birefringent component must be acquired whenit is used in the immersion lithography polarized illumination systemand phase shifting interferometry. So it is of essentiality to preciselymeasure the phase retardation distribution and fast axis azimuth angledistribution of the birefringent component.

The Chinese Laid-Open Patent Application No. 200710178950.3 discloses amethod and system of precisely measuring the optical phase retardation.By using an optical modulator in the optical setup, the modulatedpolarized light is generated. After filtering the measurement signals,the measurement of DC zero value is transferred to the measurement of ACzero value. By precisely judging the position of the extreme point, thephase retardation can be measured. But this method cannot measure thefast axis azimuth angle of the sample and the phase retardationdistribution in real time.

Tsung-Chih Yu et al. in a paper entitled “Full-field and full-rangesequential measurement of the slow axis angle and phase retardation oflinear birefringent materials”, Applied Optics, Vol. 48, p. 4568(2009),discloses a method of measuring the phase retardation distribution andfast axis azimuth angle distribution of birefringent materials by usingheterodyne interferometry method and three-step time-domain phaseshifting method. This method needs to change part of the light path tomeasure the phase retardation distribution and fast axis azimuth angledistribution in step by step and uses the time-domain phase shiftingtechnology, thus it is not feasible for measuring the phase retardationdistribution and fast axis azimuth angle distribution in real time.

SUMMARY OF THE INVENTION

The purpose of the subject invention is to overcome the shortages of theabove technology. One method and device of measuring the phaseretardation distribution and fast axis azimuth angle distribution inreal time is proposed. The measured result is immune to the fluctuationof the initial light intensity and this method has large measuringrange.

The subject application provides a device for measuring the phaseretardation distribution and fast axis azimuth angle distribution inreal time, which is composed of a collimating light source, a circularpolarizer, a diffractive component, a quarter-wave plate, an analyzerarray, a CCD image sensor and a computer equipped with an imageacquisition card. Said analyzer array is composed of four analyzerswhose polarization directions successively increase by 45°. They arerespectively named as the first analyzer, the second analyzer, the thirdanalyzer and the fourth analyzer. The positions of the above componentsare as follows:

Said quarter-wave plate is located in the same path with said firstanalyzer. And the angle between the fast axis of said quarter-wave plateand the transmission direction of said first analyzer is 45° or 135°.Light emitted from said collimating light source passes through saidcircular polarizer and said diffractive component and then is split intofour sub-beams. One sub-beam passes through said quarter-wave plate andis then analyzed by said first analyzer. The other three sub-beams aredirectly analyzed by said second analyzer, said third analyzer and saidfourth analyzer, respectively. The output port of said image sensor isconnected to the input port of said computer. The faucet for themeasuring sample is set between said circular polarizer and saiddiffractive component.

Said collimating light source is a He—Ne laser, solid state laser orsemiconductor laser.

Said circular polarizer is made of birefringent crystal, birefringentfilm or micro optical element.

Said diffractive component is a Quadrature Amplitude grating, QuadraturePhase grating or Dammann grating. The diffractive component can splitthe incident beam into four sub beams with the same light intensity.

Said quarter wave plate is a crystal wave plate, prismatic wave plate,film wave plate or composite wave plate.

Said first analyzer, second analyzer, third analyzer and fourth analyzerare all the polarizer whose extinction ratio is better than 10⁻³.

The method of measuring the phase retardation distribution and fast axisazimuth angle distribution in real time contains the following steps.

{circle around (1)} Insert the measuring sample into said faucet betweensaid circular polarizer and said diffractive component, then adjust thelight beam to let it perpendicularly pass through the measuring sample.

{circle around (2)} Turn on said collimating light source, said CCDimage sensor and said computer. Said CCD image sensor receives an imageformed by said four sub-beams and then transmits it to said computer.Said computer segregates said image into four sub-images. Then the foursaid sub-images are all pixelated and established a same coordinatesystem, respectively. The measuring sample is also matrixed andestablished a coordinate system which is the same with that of thesub-image. The intensity values in said four sub-images corresponding tothe measured matrix unit (x, y) of the measuring sample are I₁(x, y),I₂(x, y), I₃(x, y) and I₄(x, y). By calculating said intensity values,the phase retardation and fast axis azimuth angle of said matrix unit(x, y) of the measuring sample are obtained. So the phase retardationdistribution and the fast axis azimuth angle distribution of themeasuring sample can be obtained by processing said four sub-images.

Said computer processing said sub-images contains the following steps indetail:

When the polarization direction of said first analyzer is 45° relativeto the fast axis of said quarter wave plate, said computer will performthe steps {circle around (3)}, {circle around (4)}.

{circle around (3)} Said computer processes the intensity values I₁(x,y), I₂(x, y), I₃(x, y) and I₄(x, y) corresponding to said matrix unit(x, y) as follows:

${{V_{1}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\sin\left( {2{\theta\left( {x,y} \right)}} \right)}} = {\frac{2\;{I_{1}\left( {x,y} \right)}}{{I_{1}\left( {x,y} \right)} + {I_{3}\left( {x,y} \right)}} - 1}}},{{V_{2}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\cos\left( {2{\theta\left( {x,y} \right)}} \right)}} = {\frac{2\;{I_{4}\left( {x,y} \right)}}{{I_{1}\left( {x,y} \right)} + {I_{3}\left( {x,y} \right)}} - 1}}},{{V_{3}\left( {x,y} \right)} = {{\cos\left( {\delta\left( {x,y} \right)} \right)} = {1 - {\frac{2\;{I_{2}\left( {x,y} \right)}}{{I_{1}\left( {x,y} \right)} + {I_{3}\left( {x,y} \right)}}.}}}}$

Wherein δ(x, y) is the retardation of said matrix unit (x, y), and θ(x,y) is the fast axis azimuth angle of said matrix unit (x, y). Then theretardation δ(x, y) can be calculated in the range of 0°˜180° asfollows:when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}≦V ₃(x,y), the δ(x,y)=arc sin(√{square root over (V ₁²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}>|V ₃(x,y)|, the δ(x,y)=arc cos(V ₃(x,y)),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}<−V ₃(x,y), the δ(x,y)=180°−arc sin(√{square rootover (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}).

The fast axis azimuth angle θ(x, y) can be calculated in the range of−90°˜90° as follows:when V ₂(x,y)<0&V ₁(x,y)≦0,the

${{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} - {90{^\circ}}}},$when V ₂(x,y)>0, the

${{\theta\left( {x,y} \right)} = {\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}}},$when V ₂(x,y)<0& V ₁(x,y)>0,the

${\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} + {90{{^\circ}.}}}$

{circle around (4)} Sequentially change the coordinate values x and y ofsaid matrix unit (x, y) and its corresponding intensity values I₁(x, y),I₂(x, y), I₃(x, y) and I₄(x, y), and then repeat step {circle around(3)}. When the entire matrix units of said measuring sample arecalculated, its phase retardation distribution and the fast axis azimuthangle distribution can be obtained.

When the polarization direction of said first analyzer is 135° relativeto the fast axis azimuth angle of said quarter wave plate, said computerwill perform the steps {circle around (5)}, {circle around (6)}.

{circle around (5)} Said computer processes the intensity values I₁(x,y), I₂(x, y), I₃(x, y) and I₄(x, y) corresponding to said matrix unit(x, y) as follows:

${{V_{1}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\sin\left( {2{\theta\left( {x,y} \right)}} \right)}} = {\frac{2\;{I_{2}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1}}},{{V_{2}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\cos\left( {2{\theta\left( {x,y} \right)}} \right)}} = {1 - \frac{2\;{I_{3}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}}}}},{{V_{3}\left( {x,y} \right)} = {{\cos\left( {\delta\left( {x,y} \right)} \right)} = {\frac{2\;{I_{1}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1.}}}$

Then the retardation δ(x, y) can be calculated in the range of 0°˜180°as follows:when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}≦V ₃(x,y), the δ(x,y)=arc sin(√{square root over (V ₁²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}>|V ₃(x,y)|, the δ(x,y)=arc cos(V ₃(x,y)),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}<−V ₃(x,y), the δ(x,y)=180°−arc sin(√{square rootover (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}).

The fast axis azimuth angle θ(x, y) can be calculated in the range of−90°˜90° as follows:when V ₂(x,y)<0& V ₁(x,y)≦0,the

${{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} - {90{^\circ}}}},$when V ₂(x,y)>0, the

${{\theta\left( {x,y} \right)} = {\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}}},$when V ₂(x,y)<0&V ₁(x,y)>0, the

${\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} + {90{{^\circ}.}}}$

{circle around (6)} Sequentially change the coordinate values x and y ofsaid matrix unit (x, y) and its corresponding intensity values I₁(x, y),I₂(x, y), I₃(x, y) and I₄(x, y), and then repeat step {circle around(5)}. When the entire matrix units of said measuring sample arecalculated, its phase retardation distribution and the fast axis azimuthangle distribution will be obtained.

Comparing with the previous technology, the technical effect of thisinvention contains:

1. This invention can measure the phase retardation distribution andfast axis azimuth angle distribution in real time. The light intensitydistributions of the four sub-beams are the functions of the phaseretardation distribution and fast axis azimuth angle distribution of themeasuring sample. The four sub-beams are simultaneously detected by theCCD image sensor and processed at high speed by the computer, thus thephase retardation distribution and fast axis azimuth angle distributioncan be obtained in real time.

2. Fluctuation of the initial light intensity will not affect themeasured results. The initial light intensity is eliminated duringcalculation, thus the measured phase retardation distribution and fastaxis azimuth angle distribution of the measuring sample is immune to theinitial light intensity.

3. The phase retardation and fast axis azimuth angle are of widemeasurement range. Using the intensity values of the four sub-beams, thesine and cosine function of the phase retardation and fast axis azimuthangle can be calculated. Utilizing these two functions, the phaseretardation can be precisely calculated in the range of 0°˜180° and thefast axis azimuth angle can be precisely calculated in the range of−90°˜90°.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the diagram to measure the phase retardationdistribution and the fast axis azimuth angle distribution in real time.

FIG. 2 illustrates the diagram of the analyzer array.

DETAILED DESCRIPTION OF THE INVENTION

The invention is further explained in combination with the embodimentsand the accompanying diagrams, but the protection scope of the inventionshould not be limited by it.

Example 1

The diagram of measuring the phase retardation distribution and the fastaxis azimuth angle distribution in real time is illustrated in FIG. 1.The device of measuring the phase retardation distribution and fast axisazimuth angle distribution in real time is composed of collimating lightsource 1, circular polarizer 2, diffractive component 4, quarter waveplate 5, analyzer array 6, CCD image sensor 7 and computer 8. Lightemitted from the collimating light source 1 successively passes throughthe circular polarizer 2 and the diffractive component 4 and then issplit into four sub-beams. One sub-beam passes through the quarter waveplate 5 and then is analyzed by one analyzer of the analyzer array 6,while the other three sub-beams are directly analyzed by the other threeanalyzers of the analyzer array 6 without passing through the quarterwave plate 5. The CCD image sensor 7 is connected to the computer 8through electronics. The faucet for the measuring sample 3 is setbetween the circular polarizer 2 and the diffractive component 4.

The collimating light source 1 is a He—Ne laser.

The circular polarizer 2 is made of calcite crystal and quartz crystal,whose extinction ratio is better than 10⁻³.

The diffractive component 4 is a Dammann Grating which can split theincident beam into four plus or minus one-order sub-beams, whose lightintensity is equal.

The quarter wave plate 5 is a zero-order standard quartz quarter waveplate, which is located in one sub-beam's path generated by diffractivecomponent 4.

The diagram of the analyzer array 6 is illustrated in FIG. 2. It iscomposed of first analyzer 61, second analyzer 62, third analyzer 63 andfourth analyzer 64. Their polarization direction angles successivelyincrease by 45° and their extinction ratios are all better than 10⁻³.The quarter wave plate 5 is located in the same path with the firstanalyzer 61. The polarization directions of the first analyzer 61, thesecond analyzer 62, the third analyzer 63 and the fourth analyzer 64 arerespectively 45°, 90°, 135° and 0° relative to the fast axis of thequarter wave plate 5.

The computer 8 is the computer equipped with an image acquisition card.

The method of measuring the phase retardation distribution and fast axisazimuth angle distribution in real time features that it contains thefollowing steps.

{circle around (1)} Insert the measuring sample 3 into the faucetbetween the circular polarizer 2 and the diffractive component 4, andthen adjust the beam to let it perpendicularly pass through themeasuring sample 3;

{circle around (2)} Turn on the collimating light source 1, the CCDimage sensor 7 and the computer 8.

The CCD image sensor 7 receives an image formed by said four sub-beamsand then transmits it to the computer 8. The computer 8 segregates saidimage into four sub-images. Then the four said sub-images are allpixelated and established a same coordinate system, respectively. Themeasuring sample 3 is also matrixed and established a coordinate systemwhich is the same with that of the sub-image. The intensity values insaid four sub-images corresponding to the measured matrix unit (x, y) ofthe measuring sample are I₁(x, y), I₂(x, y), I₃(x, y) and I₄(x, y);

{circle around (3)} The computer 8 processes the intensity values I₁(x,y), I₂(x, y), I₃(x, y) and I₄(x, y) corresponding to the matrix unit (x,y) of the measuring sample 3 as follows:

${{V_{1}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\sin\left( {2{\theta\left( {x,y} \right)}} \right)}} = {\frac{2\;{I_{1}\left( {x,y} \right)}}{{I_{1}\left( {x,y} \right)} + {I_{3}\left( {x,y} \right)}} - 1}}},{{V_{2}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\cos\left( {2{\theta\left( {x,y} \right)}} \right)}} = {\frac{2\;{I_{4}\left( {x,y} \right)}}{{I_{1}\left( {x,y} \right)} + {I_{3}\left( {x,y} \right)}} - 1}}},{{V_{3}\left( {x,y} \right)} = {{\cos\left( {\delta\left( {x,y} \right)} \right)} = {1 - {\frac{2\;{I_{2}\left( {x,y} \right)}}{{I_{1}\left( {x,y} \right)} + {I_{3}\left( {x,y} \right)}}.}}}}$

The retardation δ(x, y) of the matrix unit (x, y) can be calculated inthe range of 0°˜180°.When √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}≦V ₃(x,y), the δ(x,y)=arc sin(√{square root over (V ₁²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}>|V ₃(x,y), the δ(x,y)=arc cos(V ₃(x,y)),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}<−V ₃(x,y), the δ(x,y)=180°−arc sin(√{square rootover (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}).

The fast axis azimuth angle θ(x, y) of the matrix unit (x, y) can becalculated in the range of −90°˜90°.When V ₂(x,y)<0& V ₁(x,y)≦0, the

${{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} - {90{^\circ}}}},$when V ₂(x,y)>0, the

${{\theta\left( {x,y} \right)} = {\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}}},$when V ₂(x,y)<0&V ₁(x,y)>0, the

${\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} + {90{{^\circ}.}}}$

{circle around (4)} Sequentially change the coordinate values x and y ofsaid matrix unit (x, y) and its corresponding intensity values I₁(x, y),I₂(x, y), I₃(x, y) and I₄(x, y), and then repeat step {circle around(3)}. When the entire matrix units of said measuring sample arecalculated, its phase retardation distribution and the fast axis azimuthangle distribution will be obtained.

The principle in detail of this invention is explained as follows.

The Jones Vector E of the circularly polarized light emitted from thecircular polarizer can be expressed as

$\begin{matrix}{{E = {\frac{E_{0}}{\sqrt{2}}\begin{bmatrix}1 \\{\mathbb{i}}\end{bmatrix}}},} & (1)\end{matrix}$

wherein E₀ is the amplitude of the circularly polarized light.

The Jones Matrix J_(S) of the matrix unit (x, y) of the measuring sample3 can be expressed as

$\begin{matrix}{{J_{s} = \begin{bmatrix}\begin{matrix}{{\cos\frac{\delta\left( {x,y} \right)}{2}} -} \\{{\mathbb{i}}\;\sin\frac{\delta\left( {x,y} \right)}{2}\cos\; 2{\theta\left( {x,y} \right)}}\end{matrix} & {{- {\mathbb{i}}}\;\sin\frac{\delta\left( {x,y} \right)}{2}\sin\; 2\;{\theta\left( {x,y} \right)}} \\{{- {\mathbb{i}}}\;\sin\frac{\delta\left( {x,y} \right)}{2}\sin\; 2\;{\theta\left( {x,y} \right)}} & {{\cos\frac{\delta\left( {x,y} \right)}{2}} + {{\mathbb{i}}\;\sin\frac{\delta\left( {x,y} \right)}{2}\cos\; 2{\theta\left( {x,y} \right)}}}\end{bmatrix}},} & (2)\end{matrix}$

wherein δ(x, y) and θ(x, y) are respectively the phase retardation andthe fast axis azimuth angle of the matrix unit (x, y) of the measuringsample 3. The Jones Matrixes J_(P) of the first analyzer 61, the secondanalyzer 62, the third analyzer 63 and the forth analyzer 64 all can beexpressed as

$\begin{matrix}{{J_{P} = \begin{bmatrix}{\cos^{2}\alpha} & {\sin\;{\alpha cos\alpha}} \\{\sin\;\alpha\;\cos\;\alpha} & {\sin^{2}\alpha}\end{bmatrix}},} & (3)\end{matrix}$

wherein α is the polarization direction angles of the analyzers. TheJones Matrix J_(Q) of the quarter wave plate 5 can be expressed as

$\begin{matrix}{J_{Q} = {\begin{bmatrix}1 & 0 \\0 & {\mathbb{i}}\end{bmatrix}.}} & (4)\end{matrix}$

After directly analyzed by the second analyzer 62, the third analyzer 63and the fourth analyzer 64 without passing through the quarter waveplate 5, the Jones Vectors E₁(x, y) of three sub-beams all can beexpressed asE ₁(x,y)=J _(P) J _(S) E.  (5)

After passing through the quarter wave plate 5 and then analyzed by thefirst analyzer 61, the Jones Matrix E₂(x, y) of one sub-beam can beexpressed asE ₂(x,y)=J _(P) J _(Q) J _(S) E.  (6)

When the Jones Matrix E₁(x, y) or E₂(x, y) is multiplied by itsconjugate transposed matrix, the intensity values I₁(x, y), I₂(x, y),I₃(x, y), I₄(x, y) of the four sub-beams corresponding to the matrixunit (x, y) of the sample 3 can be expressed asI ₁(x,y)=I ₀(1−cos(δ(x,y))),  (7)I ₂(x,y)=I ₀(1−sin(δ(x,y))sin(2θ(x,y))),  (8)I ₃(x,y)=I ₀(1+sin(δ(x,y))cos(2θ(x,y))),  (9)I ₄(x,y)=I ₀(1+sin(δ(x,y))sin(2θ(x,y))).  (10)

From equations (7)˜(10), it can be deduced that

$\begin{matrix}{{{V_{1}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\sin\left( {2\;{\theta\left( {x,y} \right)}} \right)}} = {\frac{2{I_{4}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1}}},} & (11) \\{{{V_{2}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\cos\left( {2\;{\theta\left( {x,y} \right)}} \right)}} = {\frac{2{I_{3}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1}}},} & (12) \\{{V_{3}\left( {x,y} \right)} = {{\cos\left( {\delta\left( {x,y} \right)} \right)} = {1 - {\frac{2{I_{1}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}}.}}}} & (13)\end{matrix}$Then when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over(V ₁ ²(x,y)+V ₂ ²(x,y))}≦V ₃(x,y), the δ(x,y)=arc sin(√{square root over(V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}),  (14)when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}>|V ₃(x,y)|, the δ(x,y)=arc cos(V ₃(x,y)),  (15)when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}<−V ₃(x,y), the δ(x,y)=180°−arc sin(√{square rootover (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}).  (16)When V ₂(x,y)<0&V ₁(x,y)≦0, the

$\begin{matrix}{{{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} - {90{^\circ}}}},} & (17)\end{matrix}$when V ₂(x,y)>0, the

$\begin{matrix}{{{\theta\left( {x,y} \right)} = {\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}}},} & (18)\end{matrix}$when V ₂(x,y)<0&V ₁(x,y)>0, the

$\begin{matrix}{{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} + {90{{^\circ}.}}}} & (19)\end{matrix}$

y using equations (14)˜(19), the δ(x, y) distribution can be measured inthe range of 0°˜180° and θ(x, y) distribution can be measured in therange of −90°˜90°.

Example 2

The difference between embodiment 2 and embodiment 1 is that thepolarization directions of the first analyzer 61, the second analyzer62, the third analyzer 63 and the fourth analyzer 64 are 135°, 0°, 45°and 90° relative to the fast axis of the quarter wave plate 5. And thecorresponding data processing steps are also different.

{circle around (3)} The computer 8 processes the intensity values I₁(x,y), I₂(x, y), I₃(x, y) and I₄(x, y) corresponding to the matrix unit (x,y) of the measuring sample 3 as follows:

$\begin{matrix}{{{V_{1}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\sin\left( {2\;{\theta\left( {x,y} \right)}} \right)}} = {\frac{2{I_{2}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1}}},} \\{{{V_{2}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\cos\left( {2\;{\theta\left( {x,y} \right)}} \right)}} = {1 - \frac{2{I_{3}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}}}}},} \\{{V_{3}\left( {x,y} \right)} = {{\cos\left( {\delta\left( {x,y} \right)} \right)} = {\frac{2{I_{1}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1.}}}\end{matrix}$

The retardation δ(x, y) of the matrix unit (x, y) can be calculated inthe range of 0˜180°.When √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}≦V ₃(x,y), the δ(x,y)=arc sin(√{square root over (V ₁²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}>|V ₃(x,y)|, the δ(x,y)=arc cos(V ₃(x,y)),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}<−V ₃(x,y), the δ(x,y)=180°−arc sin(√{square rootover (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}).

The fast axis azimuth angle θ(x, y) of the matrix unit (x, y) can becalculated in the range of −90°˜90°.When V ₂(x,y)<0&V ₁(x,y)≦0, the

${{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} - {90{^\circ}}}},$when V ₂(x,y)>0, the

${{\theta\left( {x,y} \right)} = {\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}}},$when V ₂(x,y)<0&V ₁(x,y)>0, the

${\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} + {90{{^\circ}.}}}$

{circle around (4)} Sequentially change the coordinate values x and y ofsaid matrix unit (x, y) and its corresponding intensity values I₁(x, y),I₂(x, y), I₃(x, y) and I₄(x, y), and then repeat step {circle around(3)}. When the entire matrix units of said measuring sample arecalculated, its phase retardation distribution and the fast axis azimuthangle distribution will be obtained.

The principle of this invention is explained as follows.

The Jones Vector E of the circularly polarized light emitted from thecircular polarizer can be expressed as

$\begin{matrix}{{E = {\frac{E_{0}}{\sqrt{2}}\begin{bmatrix}1 \\{\mathbb{i}}\end{bmatrix}}},} & (20)\end{matrix}$

wherein E₀ is the amplitude of the circularly polarized light. The JonesMatrix J_(S) of the matrix unit (x, y) of the measuring sample 3 can beexpressed as

$\begin{matrix}{{J_{s} = \begin{bmatrix}\begin{matrix}{{\cos\frac{\delta\left( {x,y} \right)}{2}} -} \\{{\mathbb{i}}\;\sin\frac{\delta\left( {x,y} \right)}{2}\cos\; 2{\theta\left( {x,y} \right)}}\end{matrix} & {{- {\mathbb{i}}}\;\sin\frac{\delta\left( {x,y} \right)}{2}\sin\; 2{\theta\left( {x,y} \right)}} \\{{- {\mathbb{i}}}\;\sin\frac{\delta\left( {x,y} \right)}{2}\sin\; 2{\theta\left( {x,y} \right)}} & {{\cos\frac{\delta\left( {x,y} \right)}{2}} + {{\mathbb{i}}\;\sin\frac{\delta\left( {x,y} \right)}{2}\cos\; 2{\theta\left( {x,y} \right)}}}\end{bmatrix}},} & (21)\end{matrix}$

wherein δ(x, y) and θ(x, y) are respectively the phase retardation andthe fast axis azimuth angle of the matrix unit (x, y) of the sample 3.The Jones Matrixes J_(P) of the first analyzer 61, the second analyzer62, the third analyzer 63 and the forth analyzer 64 all can be expressedas

$\begin{matrix}{{J_{P} = \begin{bmatrix}{\cos^{2}\alpha} & {\sin\;{\alpha cos\alpha}} \\{\sin\;{\alpha cos\alpha}} & {\sin^{2}\alpha}\end{bmatrix}},} & (22)\end{matrix}$

wherein α is the polarization direction angles of the analyzers. TheJones Matrix J_(Q) of the quarter wave plate 5 can be expressed as

$\begin{matrix}{J_{Q} = {\begin{bmatrix}1 & 0 \\0 & {\mathbb{i}}\end{bmatrix}.}} & (23)\end{matrix}$

After directly analyzed by the second analyzer 62, the third analyzer 63and the fourth analyzer 64 without passing through the quarter waveplate 5, the Jones Vectors E₁(x, y) of three sub-beams all can beexpressed asE ₁(x,y)=J _(P) J _(S) E.  (24)

After passing through the quarter wave plate 5 and then analyzed by thefirst analyzer 61, the Jones Matrix E₂(x, y) of one sub-beam can beexpressed asE ₂(x,y)=J _(P) J _(Q) J _(S) E.  (25)

When the Jones Matrix E₁(x, y) or E₂(x, y) is multiplied by itsconjugate transposed matrix, the intensity values I₁(x, y), I₂(x, y),I₃(x, y), I₄(x, y) of the four sub-beams corresponding to the matrixunit (x, y) of the measuring sample 3 can be expressed asI ₁(x,y)=I ₀(1+cos(δ(x,y))),  (26)I ₂(x,y)=I ₀(1+sin(δ(x,y))sin(2θ(x,y))),  (27)I ₃(x,y)=I ₀(1−sin(δ(x,y))cos(2θ(x,y))),  (28)I ₄(x,y)=I ₀(1−sin(δ(x,y))sin(2θ(x,y))).  (29)

From equations (26)˜(29), it can be deduced that

$\begin{matrix}{{{V_{1}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\sin\left( {2{\theta\left( {x,y} \right)}} \right)}} = {\frac{2{I_{2}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1}}},} & (30) \\{{{V_{2}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\cos\left( {2{\theta\left( {x,y} \right)}} \right)}} = {1 - \frac{2{I_{3}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}}}}},} & (31) \\{{V_{3}\left( {x,y} \right)} = {{\cos\left( {\delta\left( {x,y} \right)} \right)} = {\frac{2{I_{1}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1.}}} & (32)\end{matrix}$Then when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over(V ₁ ²(x,y)+V ₂ ²(x,y))}≦V ₃(x,y), the δ(x,y)=arc sin(√{square root over(V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}),  (33)when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}>|V ₃(x,y)|, the δ(x,y)=arc cos(V ₃(x,y)),  (34)when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}<−V ₃(x,y), the δ(x,y)=180°−arc sin(√{square rootover (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}).  (35)When V ₂(x,y)<0&V ₁(x,y)≦0, the

$\begin{matrix}{{{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} - {90{^\circ}}}},} & (36)\end{matrix}$when V ₂(x,y)>0, the

$\begin{matrix}{{{\theta\left( {x,y} \right)} = {\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}}},} & (37)\end{matrix}$when V ₂(x,y)<0&V ₁(x,y)>0, the

$\begin{matrix}{{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} + {90{{^\circ}.}}}} & (38)\end{matrix}$

By using equations (33)˜(38), the δ(x, y) distribution can be measuredin the range of 0°˜180° and θ(x, y) distribution can be measured in therange of −90°˜90°.

Experiment results show that this invention can measure the phaseretardation distribution and fast axis azimuth angle distribution inreal time. The measured results are immune to the fluctuation of theinitial intensity. Meanwhile this invention is of wide measurementrange.

We claim:
 1. A device for measuring the phase retardation distributionand fast axis azimuth angle distribution in real time, comprising acollimating light source, a circular polarizer, a diffractivebeam-splitting component, a quarter wave plate, an analyzer array, a CCDimage sensor, and a computer equipped with an image acquisition card,wherein the analyzer array is composed of four analyzers whosepolarization direction angles successively increase by 45°, they arerespectively named as a first analyzer, a second analyzer, a thirdanalyzer, and a fourth analyzer; the quarter wave plate is located inthe same path with the first analyzer, and the angle between a fast axisof the quarter wave plate and transmission direction of the firstanalyzer is 45° or 135°; light emitted from the collimating light sourcepasses through the circular polarizer and the diffractive component, andis then split into four sub-beams; one sub-beam passes through thequarter wave plate and then is analyzed by the first analyzer, the otherthree sub-beams are directly analyzed by the second analyzer, the thirdanalyzer, and the fourth analyzer, respectively; an output port of theimage sensor is connected to an input port of the computer; and a faucetfor the measuring sample is set between the circular polarizer and thediffractive component.
 2. The device for measuring the phase retardationdistribution and fast axis azimuth angle distribution in real time ofclaim 1, wherein the collimating light source is a He—Ne laser, solidstate laser, or semiconductor laser.
 3. The device for measuring thephase retardation distribution and fast axis azimuth angle distributionin real time of claim 1, wherein the circular polarizer is made ofbirefringent crystal, birefringent film, or micro optical element. 4.The device for measuring the phase retardation distribution and fastaxis azimuth angle distribution in real time of claim 1, wherein thediffractive component is Quadrature Amplitude grating, Quadrature Phasegrating or Dammann grating, which splits the incident beam into foursub-beams with the same light intensity.
 5. The device for measuring thephase retardation distribution and fast axis azimuth angle distributionin real time of claim 1, wherein the quarter wave plate is a crystalwave plate, prismatic wave plate, film wave plate, or composite waveplate.
 6. The device for measuring the phase retardation distributionand fast axis azimuth angle distribution in real time of claim 1,wherein the first analyzer, second analyzer, third analyzer, and fourthanalyzer are all the polarizer whose extinction ratio is better than10⁻³.
 7. The method for measuring the phase retardation distribution andfast axis azimuth angle distribution in real time of claim 1, comprisinginserting a measuring sample into the faucet between said circularpolarizer and the diffractive component, adjusting the light beam to letit perpendicularly pass through the measuring sample, forming an imageby the four sub-beams, receiving the image by the CCD image sensor andtransmitting the image to the computer, segregating the image into foursub-images in the computer, and processing the four sub-images in thecomputer to obtain a phase retardation distribution and fast axisazimuth angle distribution of the measuring sample, wherein the foursub-images are all pixelated and established a same coordinate system,respectively; the measuring sample is also matrixed and established acoordinate system which is the same with the coordinate system of thesub-image; intensity values in said four sub-images corresponding to themeasured matrix unit (x, y) of the measuring sample are I₁(x, y), I₂(x,y), I₃(x, y) and I₄(x, y); calculating said intensity values to obtainthe phase retardation and fast axis azimuth angle of said matrix unit(x, y) of the measuring sample.
 8. The measurement method of claim 7,wherein the computer processes said sub-images by when the polarizationdirection of the first analyzer is 45° relative to the fast axis of thequarter wave plate, performing steps of (3) and (4) by the computer: (3)processing the intensity values I₁(x, y), I₂(x, y), I₃(x, y) and I₄(x,y) corresponding to said matrix unit (x, y) as follows:${{V_{1}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\sin\left( {2{\theta\left( {x,y} \right)}} \right)}} = {\frac{2{I_{1}\left( {x,y} \right)}}{{I_{1}\left( {x,y} \right)} + {I_{3}\left( {x,y} \right)}} - 1}}},{{V_{2}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\cos\left( {2{\theta\left( {x,y} \right)}} \right)}} = {\frac{2{I_{4}\left( {x,y} \right)}}{{I_{1}\left( {x,y} \right)} + {I_{3}\left( {x,y} \right)}} - 1}}},{{V_{3}\left( {x,y} \right)} = {{\cos\left( {\delta\left( {x,y} \right)} \right)} = {1 - {\frac{2{I_{2}\left( {x,y} \right)}}{{I_{1}\left( {x,y} \right)} + {I_{3}\left( {x,y} \right)}}.}}}}$wherein δ(x, y) is a retardation of the matrix unit (x, y), and θ(x, y)is a fast axis azimuth angle of the matrix unit (x, y); calculating theretardation δ(x, y) in a range of 0°˜180° as follows:when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}≦V ₃(x,y), the δ(x,y)=arc sin(√{square root over (V ₁²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}>|V ₃(x,y)|, the δ(x,y)=arc cos(V ₃(x,y)),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}<−V ₃(x,y), the δ(x,y)=180°−arc sin(√{square rootover (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}). calculating the fast axis azimuth angle θ(x, y) in a range of−90°˜90° as follows:when V ₂(x,y)<0&V ₁(x,y)≦0, the${{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} - {90{^\circ}}}},$when V ₂(x,y)>0, the${{\theta\left( {x,y} \right)} = {\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}}},$when V ₂(x,y)<0&V ₁(x,y)>0, the${{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} + {90{^\circ}}}},$and (4) sequentially changing the coordinate values x and y of thematrix unit (x, y) and its corresponding intensities I₁(x, y), I₂(x, y),I₃(x, y) and I₄(x, y), and repeating step (3); and when the entirematrix units of the measuring sample are calculated, its phaseretardation distribution and the fast axis azimuth angle distributionare obtained; when the polarization direction of the first analyzer is135° relative to the fast axis azimuth angle of the quarter wave plate,performing steps (5) and (6) by the computer: (5) processing theintensity values I₁(x, y), I₂(x, y), I₃(x, y) and I₄(x, y) correspondingto said matrix unit (x, y) as follows:${{V_{1}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\sin\left( {2{\theta\left( {x,y} \right)}} \right)}} = {\frac{2{I_{2}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1}}},{{V_{2}\left( {x,y} \right)} = {{{\sin\left( {\delta\left( {x,y} \right)} \right)}{\cos\left( {2{\theta\left( {x,y} \right)}} \right)}} = {1 - \frac{2{I_{3}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}}}}},{{V_{3}\left( {x,y} \right)} = {{\cos\left( {\delta\left( {x,y} \right)} \right)} = {\frac{2{I_{1}\left( {x,y} \right)}}{{I_{2}\left( {x,y} \right)} + {I_{4}\left( {x,y} \right)}} - 1}}},$and calculating the retardation δ(x, y) in a range of 0°˜180° asfollows:when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}≧V ₃(x,y), the δ(x,y)=arc sin(√{square root over (V ₁²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}>|V ₃(x,y)|, the δ(x,y)=arc cos(V ₃(x,y)),when √{square root over (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁²(x,y)+V ₂ ²(x,y))}<−V ₃(x,y), the δ(x,y)=180°−arc sin(√{square rootover (V ₁ ²(x,y)+V ₂ ²(x,y))}{square root over (V ₁ ²(x,y)+V ₂²(x,y))}); and calculating the fast axis azimuth angle θ(x, y) in arange of −90°˜90° as follows:when V ₂(x,y)<0&V ₁(x,y)≦0, the${{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} - {90{^\circ}}}},$when V ₂(x,y)>0, the${{\theta\left( {x,y} \right)} = {\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}}},$when V ₂(x,y)<0&V ₁(x,y)>0, the${{\theta\left( {x,y} \right)} = {{\frac{1}{2}{\arctan\left( \frac{V_{1}\left( {x,y} \right)}{V_{2}\left( {x,y} \right)} \right)}} + {90{^\circ}}}};$and (6) sequentially changing the coordinate values x and y of thematrix unit (x, y) and its corresponding intensities I₁(x, y), I₂(x, y),I₃(x, y) and I₄(x, y), and repeating step (5), and when the entirematrix units of the measuring sample are calculated, its phaseretardation distribution and the fast axis azimuth angle distributionare obtained.